Finger-Knuckle Print (FKP) refers to the pattern obtained from the outer surface around the phalangeal joint of the finger. This image pattern has been found to contain rich lines and creases that contribute to the unique and permanent features that can be used for authentication. The hand-based biometrics such as fingerprint and knuckle print attract much attention due to high acceptability and convenience among the users. They have been found to be unique due to the presence of a large amount of distinctive information [64]. They also possess an advantage in terms of easy capturing using low-cost devices and with no requirement of an additional hardware system. Also, the acquired feature is small in size and, hence, can be used for applications involving a larger population [60]. But in countries, where a majority of the population is involved in agricultural or labourer activities, a serious damage happens to the inner part of the hand. This causes a drop in the quality of the acquired biometric sample, which further harms the feature extraction and identification process [1]. In such a scenario, features found on the outer part of the finger-knuckle print surface can be used for the purpose of authentication. The features in FKP also tend to survive longer as they lie on the outer area of the hand. The unique features of fingerprints such as minutiae and singular points have been observed to fade with time [49]. Hence, FKP can be used as a feasible biometric trait for authentication. The FKP identification system aims to find top-к matches from the database for a given probe sample. To make an identification system efficient, indexing is applied in order to reduce the search space, thereby reducing the number of comparisons [21]. Indexing is accomplished by extracting features from the FKP image and then using that feature vector for indexing.

Boosted Geometric Hashing

A geometric hashing-based FKP indexing technique has been proposed in Ref. [28]. The proposed technique has boosted the geometric hashing such that the extracted feature is inserted into the hash table exactly once. The first step is to extract features from the FKP image. In the proposed technique, feature vectors have been constructed by determining the key points through two methods called, Scale Invariant Feature Transform (SIFT) [41] and Speeded-Up Robust Feature (SURF) [6] and, then forming descriptors around these key points. SIFT identifies those features that remain stable at different scales. Such key points are identified using the difference of Gaussian (DoG) function. To make the feature robust to image rotation, orientation of the key point is also determined. SURF features are extracted using two major steps, key-point detector and key-point descriptor. Key-point detection is done using the Hessian matrix. The key points are detected at different scales, and the non-maximum suppression is applied in 3 x 3 x 3 neighbourhood to localise the key points. The descriptor is computed by using a rectangular window around each key point. This window is split into 4x4 sub-regions, and the Haar wavelet responses are extracted from them. The descriptors obtained from all the sub-regions are then concatenated to form a single descriptor. The generated SIFT and SURF feature descriptors are of length 128 and 64, respectively.

Indexing: Every feature vector fi extracted using SIFT and SURF is represented by (Xj, y„ D), where xi and yi denote the coordinates and D, represents the feature vector. The coordinates of the feature vectors have been used for index generation of the hash table. The descriptor D, has been used for recognition. Three steps have been followed to make the proposed technique robust to translation and rotation. These are (i) mean centring, (ii) feature rotation utilising the principal components, and (iii) normalisation. Sometimes, the features extracted from FKP images of the same subject taken at different times may not have the same coordinate position. Mean centring is done to handle this type of noise. It is accomplished by taking average of all f/s, denoted by fh and subtracting it from each feature vector. Therefore, the new coordinate position of f = f - f is given by (jq, у• ]. In the second step, the feature vectors are rotated in such a way that they all become aligned in a uniform coordinate system. Principal component analysis (PCA) has been used to determine the primary axes of the coordinate system. The coordinates of the features are then rotated in a manner that they become aligned along the determined X and Y axes. Lastly, normalization is done to account for scaling. In this step, the normalised coordinates of every feature vector are computed, and a scaling factor is multiplied to these coordinate values to avoid falling of all the coordinates in one single bin. The hash table is aligned with respect to the normalised coordinate system, and the feature vectors along with their FKP id are stored in the table. The hashing process is shown in Figure 11.8 (image taken from [28]).

Retrieval: During the retrieval phase, a query FKP image is shown to the identification system, and the same procedure of feature extraction is carried out for

Boosted geometric hashing. Hash table showing entries with principal components as a basis

FIGURE 11.8 Boosted geometric hashing. Hash table showing entries with principal components as a basis.

this image as well. Let us consider for a query FKP image Q, n features have been extracted. The extracted features are mapped to a bin for candidate set retrieval. Neighbouring bins of size к x к are also considered to account for missing or spurious features. Euclidean distance is computed between the features of the retrieved candidate and query. Therefore, corresponding to every feature, a candidate set will be retrieved, making a total of n candidate lists. These lists are concatenated and IDs are sorted in decreasing order of their number of occurrences.

11.4.2 Results

The proposed technique has been tested on PolyU Finger-Knuckle Print (FKP) database [23]. The (PolyU)FKP is a publicly available data set containing finger-knuckle print images collected from 660 subjects. Each subject has provided 12 samples which have been collected in two separate sessions with a gap of 25 days. It, thus, comprises 7,920 images in total. Some of the images are shown in Figure 11.9. The first 11 images, out of 12, have been used for indexing, while the remaining one has been used as a query image to the identification system. Correct recognition rates (CRRs) of 96.36% and 99.69% have been reported with SIFT and SURF features, respectively. The technique has achieved 99% hit rate at 10.62% and 94.07% penetration rates when SURF and SIFT features were used, respectively.

The proposed technique has also been tested for robustness to occlusion and rotation in the FKP images. To do so, FKP images have been artificially occluded by 1%, 4%, 9%, 16%, 25%, and 36% as shown in Figure 11.10a. The occluded images have been divided into 2x4 sub-blocks, and the SIFT and SURF features are extracted from each sub-block. These blocks are compared separately and their matching scores are combined to form a matching decision. The graph between hit rate and penetration rate for various levels of occlusion as shown in Ref. [28] provides two observations. First, SUFT has better features for occlusion as it has around 95% hit rate at 5% penetration rate with low occlusion, whereas SIFT achieves 95% hit rate at around 40% penetration rate when occlusion is very low. Second, SURF is more robust to occlusion, as the hit rate does not change much for l%-38% of the occlusion. Flowever, with SIFT feature, hit rate decreases from 90% to 30% at 10% penetration rate when occlusion is varied from 1% to 38%.

To test the proposed technique’s robustness against rotation, different degrees of rotation (0°, 10°, 50°, 110° and 150°) have been introduced in the FKP images, as shown in Figure 11.10b. The graph between hit rate vs. penetration rate for various

Sample FKP images from PolyUFKP database. First row samples are collected in the first session and the second row contains corresponding images collected in the second session

FIGURE 11.9 Sample FKP images from PolyUFKP database. First row samples are collected in the first session and the second row contains corresponding images collected in the second session.

Occlusion and rotation on FKP [28]

FIGURE 11.10 Occlusion and rotation on FKP [28].

degrees of rotation as shown in Ref. [28] shows results as expected. As it is known that SIFT and SURF are both rotation-invariant features, artificially introduced rotation does not deteriorate hit rate at any penetration rate.

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